At the time of his submission of the notification procedure, we had expressed our concerns to the building authority in writing because the basement depth exceeds our foundation by 30 cm.
The building regulation office, as the deciding authority, naturally saw no reason for a construction stop since all the requirements of the development plan were met and the documents were complete - BUT it was strongly pointed out that the stability of our building and the subsoil must be considered. The architect and the creator of the structural stability certificate were also informed of this again by phone.
Our neighbor apparently sees this letter as a free pass for everything - his response to our message was to send this document as a PDF without comment - although we already have it, of course.
However, this only has relevance in terms of building law - what also needs to be considered under private law is simply ignored.
Fortunately, I get along quite well with our building authority - they have or will clearly point out again that he cannot simply do whatever he wants. Of course, I have also provided them with our letter. He seems to listen to or believe the building authority.
He also actually has a foundational problem with his other neighbor. That neighbor has insulation of the basement slab at 2.90 m, which apparently lies in gravel. That would then simply spill out sideways.
Therefore, professionals would be needed for this construction gap - which unfortunately do not seem to be available here.